Question

Consider the decay of Cs 137, Ba"37," ? Ba137 (stable) ? 30.0 years 2.55 min The decay scheme is given below. 1.174 MeV max B rays have an average energy of 0.395 MeV, whereas the 0.512 MeV max ß rays have an average energy of 0.173 MeV. Initially a sample of 2.5 kg of pure Cs137 is placed in a container that absorbs all the out-coming B and y rays. osujuev (95%) p- 0.662 Mevy (1.174)v What is the initial required cooling rate (in W) to be applied to the container to maintain its temperature fixed? What will be the required cooling rate the next day Good Luck

Answer 1

Half life is CS^137 lambda = 30.0 years = 30.0 times 3.154 times 10^7 s = 9.462 times 10^8 s Therefore Decay constant pf CS^137 = lambda_1 = ln 2/T_1 lambda_1 = ln/9.462 times 10^8 s^- 1 lambda_1 = 7.3256 times 10^- 10 s^- 1 Half life of Ba^137, T_2 = 2.55 min = 2.55 times 60 s = 153 s Therefore decay constant of Ba^137: lambda_2 = ln 2/T_2 = ln 2/153 middot s^- 1 lambda_2 = 4.5304 times 10^- 3 s^- 1 Number of atom in 2.5 kg of pure cs^137 n_0 = 6.022 times 10^23/137 times 2500 N_0 = 1.0989 times 10^25 Therefore Initial rate of decay of Cs^137 is magnitude dN/dt = 7.3256 times 10^- 10 times 1.0989 times 10^25 dis/s = 8.0501 times 10^15 dis/s Therefore rate at whiole energy is released